Mat 113 Lecture 5Outline of Last Lecture 1. How to do conversions of different unitsA. Example Problem2. Geometry FormulasOutline of Current Lecture 3. Simpson’s Paradox 4. ExampleCurrent Lecture3. Simpson’s ParadoxThis occurs when:- When combining, or aggregating, data masks underlying patterns - When a factor distorts the overall picture, but distortion goes away when underlying data is examined 4. Example The following data shows the hitting records of two major league baseball players for 1995 and 1996. Complete the batting averages, which are usually as a decimal to 3 places. Then answer the questions at the bottom. 1995 1996Jeter- 48 At Bats, 12 hits Jeter- 582 At Bats, 183 hitsJustice- 411 At Bats, 104 hits Justice- 140 At Bats, 45 hits To find the batting averages, you would take the hits and divide them by their at bats. Which would equal, .250 for Jeter in 1995 and .253 for Justice in 1995. In 1996, .314 was Jeter’s average and .321 was Justice’s average. Question 1: Which batter had the higher average in 1995? These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Answer: JusticeQuestion 2: Which batter had the higher average in 1996?Answer: JusticeQuestion 3: Which batter had the higher average over the 2-year period? (To find this answer you would add the hits from both years together and divide it by the added number of at bats for both years). Jeter’s Average = .310Justice’s Average = .270Answer: Jeter had the higher average over the 2-year periodThe answer to the last question is not aligned with the answers to the first couple of questions, because it looks as if though Justice would have the higher average over the 2 year period, but Jeter actually does. This is why it is a Simpson’s